In “dual-high” power systems, the lack of inertia and reserves makes frequency security a prominent concern. Embedding frequency constraints and coordinating the optimization of heterogeneous frequency regulation resources in dispatch are effective solutions. Therefore, this paper proposes a distributionally robust frequency constrained unit commitment optimization scheme considering load-side frequency support. First, the system frequency response process is analyzed, and a system frequency response model considering load-side frequency support is established, from which a set of frequency security constraints is constructed. Second, the uncertainty of renewable energy is characterized using fuzzy sets based on the Wasserstein distance, and a distributionally robust optimization model for unit commitment that includes frequency constraints is formulated. Due to the highly non-convex nature of the proposed model, a two-stage decomposition algorithm is employed for iterative solution. Additionally, an adaptive multi-directional cut-plane method is proposed to effectively link the master and subproblems. Finally, case studies are conducted based on modified IEEE 39-bus and IEEE 118-bus test systems. The results demonstrate the necessity of incorporating frequency constraints and the importance of load side frequency support in renewable energy power system dispatch schemes, validating the effectiveness of the proposed unit commitment scheme and the superiority of the solving method.